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Nonlinear Phenomena pp 402–415Cite as

Order in the Chaotic region

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Part of the book series: Lecture Notes in Physics ((LNP,volume 189))

Abstract

A simple algorithm is constructed for the quadratic one-parameter family of maps. It predicts the number of periodic orbits of arbitrary period ocurring for parameter values lower than any other corresponding to a given stable periodic orbit. This algorithm produces the number of periodic unstable points coexisting with the stable periodic orbit. This method associates an important polynomial in a one-to-one correspondence with the symbol of Metropolis et al. for ordering the periodic orbits, with the permutation matrix of the dynamics of points in the stable cycle, and with the matrix of regions separated by these points.

These polynomials coincide with those polynomials used by many authors in connection with the triangular map and with the topological entropy.

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Authors and Affiliations

  1. Departamento de Física, Universidad Autónoma Metropolitana, Iztapalapa D. F., Mexico

    Eduardo Piña

  2. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Zacatenco, D.F., México

    Eduardo Piña

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  1. Eduardo Piña
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K. B. Wolf

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© 1983 Springer-Verlag

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Piña, E. (1983). Order in the Chaotic region. In: Wolf, K.B. (eds) Nonlinear Phenomena. Lecture Notes in Physics, vol 189. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12730-5_23

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  • DOI: https://doi.org/10.1007/3-540-12730-5_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12730-7

  • Online ISBN: 978-3-540-38721-3

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